Which of the following numbers is a multiple of 4? ${47,67,100,103,113}$
Solution: The multiples of $4$ are $4$ $8$ $12$ $16$ ..... In general, any number that leaves no remainder when divided by $4$ is considered a multiple of $4$ We can start by dividing each of our answer choices by $4$ $47 \div 4 = 11\text{ R }3$ $67 \div 4 = 16\text{ R }3$ $100 \div 4 = 25$ $103 \div 4 = 25\text{ R }3$ $113 \div 4 = 28\text{ R }1$ The only answer choice that leaves no remainder after the division is $100$ $ 25$ $4$ $100$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $4$ are contained within the prime factors of $100$ $100 = 2\times2\times5\times5 4 = 2\times2$ Therefore the only multiple of $4$ out of our choices is $100$. We can say that $100$ is divisible by $4$.